# Straights

In poker, a *straight* is a continuous
sequence of cards, in this case of any length. Your friend John
makes up a game called straights which is played with
$N$ cards with numbers
that may repeat, between $1$ and $10^4$. In order to win, you must get
rid of all of your cards in as little turns as possible. The
only way to put down more than $1$ card at a time is if the cards are
strictly in *descending* or *ascending* order.

For example, given eight cards with the numbers: `1 8 3 6 5 7 2 1`, the minimum number of turns to
get rid of all of your cards would be: `3` because you would have 2 straights:
`1 2 3` and `5 6 7
8` and a single card: `1` left
over.

Can you find the minimum number of turns required for you to win?

## Input

Input consists of two lines. The first contains the number of cards that you are given $N$ ($1 \leq N \leq 10^4$). The second line consists of $N$ space separated integers each with a value between $1$ and $10^4$.

## Output

Output the minimum number of turns to win.

Sample Input 1 | Sample Output 1 |
---|---|

8 1 8 3 6 5 7 2 1 |
3 |